Question

Question 4 (ivW
hich of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically:
2x - 2y - 2 = 0, 4x - 4y - 5 = 0

Answer 1

2x - 2y - 2 = 0, 4x - 4y - 5 = 0
Comparing these equations with
$a_{1}x+b_{1}y+c_1=0$
$a_{2}x+b_{2}y+c_2=0$

We get
$a_1=2,b_1=-2,and{c}_1=-2$
$a_2=4,b_2=-4and{c}_2=-5$

$\frac{a_1}{a_2}=\frac{2}{4}=\frac{1}{2}$
$\frac{b_1}{b_2}=\frac{-2}{-4}=\frac{1}{2}$ and
$\frac{c_1}{c_2}=\frac{2}{5}$
Hence, $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
Therefore, these linear equations are parallel to each other and thus, have no possible solution.
Hence, the pair of linear equations is inconsistent.